Mathematics – Probability
Scientific paper
2011-08-31
Mathematics
Probability
30 pages, 6 figures
Scientific paper
We use a multitype continuous time Markov branching process model to describe the dynamics of the spread of parasites of two types that can mutate into each other in a common host population. Instead of using a single virulence characteristic which is typical of most mathematical models for infectious diseases, our model uses a combination of two characteristics: lethality and transmissibility. This makes the model capable of reproducing the empirically observed fact that the increase in the host density can lead to the prevalence of the more virulent pathogen type. We provide some numerical illustrations and discuss the effects of the size of the enclosure containing the host population on the encounter rate in our model that plays the key role in determining what pathogen type will eventually prevail. We also present a multistage extension of the model to situations where there are several populations and parasites can be transmitted from one of them to another.
Borovkov Konstantin
Day Robert
Rice Timothy
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